Relatedly, make sure you trigger the password lock on your device before handing it over. They may be able to compel you to give your biometrics but not your password (the latter is considered compelled speech, and the courts have not fully litigated whether the former is treated the same).
Nova Launcher on Android (and maybe other launchers, I do not know) has a nifty little feature to activate password lock bypassing biometrics with a gesture. Which comes in handy everytime I go through the border.
At least on Android, turning off or restarting your phone will work as well. Because you must enter your pin or password upon first starting up rather than use biometrics. At least, that seems to be the default. It may be a setting somewhere to turn that off.
